Ames Laboratory ISC Technical Reports Ames Laboratory
Electrical properties of thin metallic films
D. B. Barker
Iowa State College
W. C. CaldwellIowa State College
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Electrical properties of thin metallic films
The Hall coefficient and conductivity of silver films were measured by a DC method and comparisons with the theoretical calculations of Fuchs and Sondheimer were made. Films from 150 A. to 1500 A. in thickness were deposited by evaporation at pressures below 10^-2 microns. The electrical properties were studied at liquid nitrogen, dry ice and acetone, and room temperatures. Film thickness measurements were made by the interferometer method. Electron diffraction and electron micrograph pictures were taken to study agregation and to check on the purity of the films. The electron micrographs show aggregation in films less than 300 A. thick. The electrical measurements also indicate this change in the thinnest films. A variation of Hall coefficient and conductivity with thickness was found but only qualitative agreement between theory and experiment was indicated.
Other Physics | Physics
OF THIN METALLIC
March 20, 1952
Reproduced dire(!t from copy a.s submitted to this office.
PRll'JTE.D IN USA PRICE 2Cl CENTS A.vailab:i.e fran;. the Office of Technical Services
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Work performed under Contract No. 'w-740)-eng-82.
ELECTRICAL PROPERTIES OF THIN METALLIC FILMS
D. B. Barker and W. C~ Caldwell
The Hall coefficient and conductivity of silver films were measured by a DC method and comparisons with the theoretical
calculations of Fuchs and Sondheimer were made& Films from
150 A. to 1500 A. in thickness were deposited by evaporation at
pressures below lo-2 microns~ The electrical properties were
studied at liquid nitrogen, d~ ice and acetone, and room
temperatures~ Film thickness measurements were made by the
interferometer method~ Electron diffraction and electron
micro-graph pictures were taken to study agregation and to check on
the purity of the films. The electron micrographs show
aggre-gation in films less than 300 Ao thick.. The electrical
measure-ments also indicate this change in the thinnest filmso A variation of Hall coefficient and conductivity with thickness
was found but only qualitative agreement between theory and
experiment was indicatedo
Theoretical calculations of the electrical characteristics of bulk
metals are made3 in the simplest case~ in terms of the free electron
theory (1). The calculations are essentially classical9 assumine only
from the quantum approach that the electron energies are proportional to
the square of the wave vector, kj and that these energies are distributed
according to Fermi-Dirac statistics~ The conduction electrons are assumed
free to migrate with thermal energy through the lattice.? undergoing collis-.
ions much as molecules in a gaso The effects of the collisions at the
surface of the solid are assumed to be negligible compared to those within.
The average distance of el.e ctron travel between collisions is defined as
the mean free path~
If any dimension of a metallic conductor approaches in magnitude the
mean free path lengthj as is possible in evaporated films, surface effects
must be consideredo Fuchs (2) has made an analysis of this condition for
the case of plane films with an electric field applied parallel to the
critical surfaces. His calculation was similar
wthat performed for
bulk materials except that new boundary conditions were applied for the
For the simplest case9 Fuchs assumed that all electrons striking the
surfaces vmre scattered diffusely 1d th a complete loss of their drift velocities. The resulting equations were solved numerically in terms of the ratio of the bulk metal conductivity,
,to the thin film conducti-vity, cr and the ratio of the film thicknesg_, a, to the mean free path length,JL e A graphical presentation of the solution is shown in
Fuchs obtained a more complete roJution by ~ing a p:n-ameter~ E. , Wlich represented the fraction of the electrons that reflected specularly at the surface. As £ approaches one, the curve in Fig. 1 approaches a horizontal line corresponding to a conductivity ratio of unity.
Sondheimer (3) has extended this analysis for the case of a magnetic f:i.eld perpendicuJa r to both the critical surface and the electric field., The same assumptions were made and the methods of solutions similaro For low magnetic fields (up to 15 or 20 kilogauss) Sondheimer0 s solutions for the conductivity ratios agreed with those obtained by Fuchso At high
fields he found that the conductivity oscillates as the field is increasedQ SondheimerVs solution for the ratio of the thin film Hall coefficient, A~ to the bulk metal coefficient3 ~o.? with diffuse reflection of the electrons and low magnetic fields, is shown in Figo 2. His parameter p, has the same significance as €9 as p approaches one,:~ this curve also drops to a value of unity.
Since the electronic mean free path for even the best conductors is _about
500A., very thin films are necessary to study these effects. Such
films may be prepared by chemical deposition, sputtering.., or evaporation .. Of these three processes, evaporation is the simplest and most rapid.
A few films of gold were deposited for an initial investigation, but the principal study has been made with silvero Silver is easily evaporated, is not highly active chemically, has a large electronic mean free path, and has bulk. conductivity· properties in agreement with calculations. based on the free electron theory. These characteristics make silver a particularly suitable metal for studying thin filmsc
EVAPORATION OF FILMS
Glass microscope slides were used as substrates for the films.· Just before use~ these were carefully cleaned in Dichromate cleaning solution and then with Dreft suds in distilled water~ They were rinsed with several hundred milliliters of boiling distilled water from a wash bottle and
allowed to dry in a dust free atmosphere~ All handling was done with forceps.
15 12 10 7
s~4 tT 3 2
.02 .05 .I
THEORETICAL CURVE (FUCHS € = 0 )
FOR FILM SERIES 130 140
AT ROOM TEMPERATURE - -
--o---AND LIQUID NITROGEN
\\o o, \
... ~ ...
FIG. I. ELECTRICAL CONDUCTIVITY OF THIN SILVER FILMS.
AH0 1.3 1.2 1.1 1.0. 1 ..._<» ct .2
I '+ I \ ~ ct
\ 0 \
(SONDHEIMER P= 0)
SERIES 130 14 0
RO 0 M TEMPER AT URE
--+---0--LIQUID NITROGEN TEMPERATURE e ( )
' O' 0
... 'b <2.o
HALL COEFFICIENTSOF THIN SILVER FILMS.
~-- Gloss slide
Conductivity probe placed
here. ---t--1;:~ _ _.
Fig. 3. Arrangement of ailver film on glau alide.
8-Voltage drop for
conductivity. C-Hall voltage
0-Volta~e drop for
cur rent value.
0.1 ohm Standard Reaiator
Ff~. 4. Circuit far electrical meaauremenh.
Ma~netlc field perpendicular to plane of film.
A filament was constructed
qywinding approximately two feet of 0.010
in. diameter~ 98~% purity, Makepeace~ silver 1dre on a 6 or 7 turn~ 0.3 ine
diameter, tungsten helix of 0~030 in~ diameter wire., A coil of 0.008 in. diameter molybdenum wire was loosely wound over the silver. When the
silver melted~ surface tension caused it to form membranes stretched bebreen the tungsten and molybdenum wL res~ The filament was thus able to
hold a greater charge of silver and more surface area was provided for
After the filament and shielded substrates had been loaded into the
vacuum chamber and a vacuum of about 100 microns had been attained~ a gas discharge of 70 rna. at about 3000 volts was maintained for 15 mine to further clean the substrates by ion bombardment~
When the. vacuum had reached 1 micron a shutter was swung between the filament and the substrates
qymoving a magnet outside the bell jar. Then
the filament was heated just above the melting point of silver for
5to 10 sec. to prefuse the silver and outgas the filament structure~
Following this~ the system was allowed to pump for 10 to 12 hours to allow further outgassing. At the end of this time the vacuum was below
the minimum gauge readings lo-2 microns, The shutter was then opened
and the films deposited by heating the filament to the evaporation point for 10 sec. or less.)) depending on the film thicknes.ses desired., During 2
,this heating the gauge continued to indicate a pressure of less than
Three sets of films including thicknesses from 150 to 1)00 A. were
prepared by this method and labeled series 130, 140, and 150. The films
were stored in a dessicator at normal pressures and temperatures except
while measurements were being madee
All electrical measurements were made with the simple DC potentiometer circuit shown in Fig.
4.A Rubicon, Type B Potentiometer was used with a
Rubicon~ lamp enclosed type galvanometer having a sensitivity of 0.02 microam:ps & per mm9
For the measurements, the substrate was mounted on a small masonite
board,Which had been sprayed with plastic for waterproofingo Current
contact with the film was made through flat, phosphor-bronze clips and connections for Hall voltage and conductivity were made with spring-brass wire clips. It was found necessa~ to place several layers of aluminum
foil between each clip and the evaporated silver contacts to attain a
also provided excellent contact at room temperature but tended to flake off When the assembly was cooled~
The electrical measurements were made in two stages~
First~ a film was mounted in the holder and the assembly placed
in the magnetic fieldo A current of 0~01 ampso to 0.2 amps. was allowed to flow for several minutes to insure that a stable condition existede No heating of the film was ever detectedo Readings were then taken of the voltage drop across the film, the voltage drop across
the standard resistor, and the Hall voltage. The Hall voltage
measure-ment was repeated with the magnetic field reversedo Three sets of
data were taken with the order of the readings varied in order to
eliminate any residual voltage drift effectso The film and holder were then immersed in liquid nitrogen contained in a dewar located
between the poles of the magnet and the series of measurements repeated at this temperatureo After being removed from the liquid
nitrogen, the sample was warmed to room temperature and the condensed
moisture evaporated off by a small blotver., The room temperature measurements were repeated to check for any irreversible effects of
After being stored in a dessicator for a period of time from one
to three weeks9 the film was remounted in the holder and carried through a similar process with the liquid nitrogen being replaced by
a dry ice and acetone mixtureo · A polyethylene bag was used to protect
the film and holder from the destructive effect of the acetone. Since
the Hall coefficient changes only Slightly between room and dry ice
temperatures the Hall measurements were not repeatedo
Later, several of the films were mounted in the holder at room
temper-ature, measured, dismounted, and then the cycle repeated several times to
check the reproducibility of the measurementso
FILM THICKNESS MEASURE:MENTS
After all electrical measurements had been completed the thickness of
each film was measured by the interferometer method that has been adequately
discussed and described by Tolansky
(4).The step in the film was produced by making a scratch with the sharp corner of a microscope slide. This
produced a sharp break in the film without damaging the substrate.b
Some evidence was obtained to indicate that errors can be introduced into the thickness measurements if the top layer of silver is more than
800 or 900 A. thicko This problem should be studied furthero
The equipment used here for these measurements has been described by
ELECTRON DIFFRACTION AND MICROSCOPY
A study of some of the chemical and physical properties of the thinner films was undertaken to check the continuity and purity of the films.
Samples for study were obtained by placing on each substrate several nickel,
electron-microscope screens covered with a thin collodian filmo Sennett
and Scott (6) have indicated that the physical character of deposited
films is the same for all smooth~ amorphous substrates so a film on
collodian will reveal the nature of the film on glass. The covered screens
were examined in an RCA~
EMUElectron Microscope which could be used for
either microscopy or diffraction.
EXPERIMENTAL RESULTS ·
The electron microscope screens were examined immediately following the deposition of the films 11 after several ••eeks aging, and after immersion
in liquid nitrogen~ The diffraction studies revealed a small amount of
impurity which has been tentatively identified as
wo3 in the films of series
130 but none in the films of the other serieso This is presumably due to
the fact that the tungsten filament was maintained at a higher temperature anQ for a longer period of time for the series 130 evaporation than for
The electron micrographs of the films were similar to those of Sennett
and Scott. Aggregation was evident in films below 200 A • in thickness,
although enough contact ~vas maintained between the individual particles to
allow films as thin as 1~0 A, to conduct. The particles'of the films thinner
than l50A., were about lOOA. 1.n diameter.
No changes were noticed in the films after aging or immersion in liquid nitrogen. The effects of immersion on films deposited on collodian
and on glass are probably different however because of the differences in
the expansion coefficientso
Summaries of the results of the electrical measurements are shown
plotted in Figs.
6.The thickness of each film was measured to within
3%or less. At any one time the electrical measurements could be
reproduced to within 2%. Over the period of aging and i1nmersion some
values changed as much as
5%11 however no trends predominated in the changes
of the Hall coefficients or the conductivities; some varied monotonica~
up or down~ some randomly~ and some not at allo
The values for the resistivity of bulk silver shovm in Fig.
5were taken from The Handbook of Chemist~ and Physics (7)o The values for the
Hall coefficient of the bulk material in Table I were averaged from those
given in The International Critical Tables (8).. In Table I are given the
8ULK SILVER +
-50 100 150 200 250 300
FIG. 5. TEMPERATURE DEPENDENCE OF RESISTIVITY OF THIN SILVER FILMS
Electrical Constants for Bulk Silver
Temperature (°K) 77 19.5 29.5
Po(ohm-em) o38(lo-6) L02.(lo-6 ) 1 .. 60(10-6)
c~/coulomb) .92.(10-4) ,.BB(lo-4) o84(lo-4)
/ (cm2/volt-sec) 240 86
(electrons/c~)6.,8 (lo22) 7" 1.( lo22 ) 7o4(lo22 ) nl/3 (1/cm) 4ol (10
,~e. (Angstroms) 4.50 710 2000
It is int~resting to note that for the linear portion of the curves in Fig. 6, the change in Hall coefficient with temperature is nearly the same as for bulk materials and that the change is independent of thicknesse If the Sondheimer prediction were true, one would expect the change to be larger for the thinner films~
The sharp break in the region of 300 A~ in the curves which show conductivity or Hall effect as a function of thickness is probably due to aggregation causing a physical change in the filmse In this region the data are a function of the contact between particles as well as the
properties of the particles themselves. A project is now being planned in which films will be deposited on substrates at liquid nitrogen temper-atures and maintained at that temperature while electrical measurements are made ..
~~ 10 E
:J: ~ 0.81 0 I
SERIES 130 140 150
~---.---~-';,-.o __________ <.._ -o-2..o ____ - - - --~-:!---~-~ -~-:!---~-~
200 400 600 800 1000 1200 1400 1600
Thickness, a, (A)
FIG. 6. HALL COEFFICIENTS OF THIN SILVER FILMS.
1.. Seitz9 F~ The Modern Theory of Solids. N.Y~, HcGraw-Hill Book Co.,
Inc. 1940.- - .
2., Fuchs, K& Proc., Camb. Phil. Soc.
J,. Sondheimer~ E. H. Phys. ·Rev.
..Tolansky, S. Multiple-Beam Interferome!:.!z. Oxford, The Clarendon Press. 1948.
5.Bearinger, V. W. ~ Comparison of Methods of Measurin~ the Thiclmess of Thin Metal Films, Unpublished Ph.D. Thesis.- Ames, Io-vm, Iowa · Stateeollege·"Library. 19.50.,
eSennett, R. So and Scott, G.D. J. Opt •. Soc.Am.
7. Handbook of Chemistry and Physics. 27th Edo Cleveland, Chemical Rubber Publishing Co~ 1943o
8~ International Critical-Tables of Numerical Data, Physics, Chemistry, and Technolo~~ New York, McGraw-Hill Book Co~, Inco 1929.